{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"http://hilpisch.com/tpq_logo.png\" alt=\"The Python Quants\" width=\"35%\" align=\"right\" border=\"0\"><br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Derivatives Analytics with Python"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**_Chapters 12 & 13_**\n",
    "\n",
    "**Wiley Finance (2015)**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"http://hilpisch.com/images/derivatives_analytics_front.jpg\" alt=\"Derivatives Analytics with Python\" width=\"30%\" align=\"left\" border=\"0\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Yves Hilpisch\n",
    "\n",
    "The Python Quants GmbH\n",
    "\n",
    "<a href='mailto:analytics@pythonquants.com'>analytics@pythonquants.com</a>\n",
    "\n",
    "<a href='http://pythonquants.com'>www.pythonquants.com</a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Chapter 12: Valuation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 0.000000\n",
      "         Iterations: 270\n",
      "         Function evaluations: 485\n"
     ]
    }
   ],
   "source": [
    "%run 12_val/BCC97_simulation.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3225.930000, -0.000320, 0.146849, 0.104511, 0.175197])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.array((S0, r0, kappa_r, theta_r, sigma_r))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([22.211918, 0.024776, 0.952100, -0.999156, 0.036057, 0.008426,\n",
       "       -0.501069, 0.000000])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "opt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Simulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Db9TIriZIC5fLTj4MCYHDh21DrVMnO1QTYL7f8j295vViymNTuP/m+/0bTEyM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jgPfQtoBoa97SGgXkR8qprM2K8pY5/UfuN2FZj8+eCDD/JdhIJndZx7Vsczw+p59pnxywBF5CCw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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb9325ea050>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_rate_paths(r)\n",
    "plt.savefig('../images/12_val/rate_paths.pdf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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7sGCBuRE6FmF/++2wciXUW+HGTsppKoLTklmhs4hLj6Oqrv0IeUNUvXEUsb+/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177UCTvmCEc33O06P3f2irLmD7dfERMXTe1S+f23HNCvP228bIlO5eIpzc8Lfz9/S2WaXYFWq0Q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\nONbR8XR0P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DNnAHAq24NPn8X09Oxptupvv8lBhJ8fODgEo1bXoNFICkrm5W3MesffEXEH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\nioqKisolimrkVVRUVFRULlH+H3TjEdMsSY29AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb9321016d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_volatility_paths(v)\n",
    "plt.savefig('../images/12_val/volatility_paths.pdf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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LYCfgVeJHgA+llP8WQlwFPAF8WQixAMiXUl4phAgGDgohCoBW4CVgmZSyVgjx\nBHAL8Lyfy63RaIYJt1u924uKVCouVsvDh5Uv1IIFStgfekitR0cPd4lHKE1N3UXdu26xdM0Pz81V\nnoy5uUpQ/R2VTkoVuefHP1aOcnff3b0x0dbWJf7eVFDQtX78uIqI1LMxkJSkGjFecQ8O7hL1O+5Q\n4XdHjz4jcZdSUud0dhN0b2p0OpkUEUGOkW5KTSUnMpJss5mwYYjw57cevhDiJqANmAFESinvE0Ic\nAy6UUlYavf0iKWWiEOIXgF1K+bBx7pvAs8ABlHUgy9j+WeAmKeX1vdxP9/A1mhGCx6M6WT1FvahI\nxVZJTlYW4Z5p8mRtnj9tGhq6C7p3va2tS9S94+tTp6pe8nCEmz12TIUubGpSHyeYOvX0r+HxqMA2\nx46pYDrehkBtrfrxeEX+DMTdIyUVDgcHfEXdWPcAuV5hj4zsFPgJ4eEE+dEjNCB6+EKIXCBHSvkj\nIcRMwFugFMBqrFuAeKNHnwwc9LmExTi2zud4jPUBTorUaDTDSXu7EvWKCvX9D19RLy2FhITuYn7x\nxWqZkaED3JwR9fXdPeK94m6zdRf1K69Uy7FjA2N6gpTw3HMqtv33vqe+bHemYW6DgiAtTaUFC87o\nEm1uN0fa2znU3s5hY3movZ0im424kJBOUZ8VFcWNKSnkRESQGhaGCIS6PAX+MulfC9iFEPcDC4Ew\nIcR3gFogBiXoMUCTlNIthKhFjd97iQFOGMf33F7b101XrVpFeno6AHFxceTl5XWOIXm/zazzZ57f\nvXs33/3udwOmPOdi3rstUMrTV/6DDwqoq4PRo/M5fhzWr1d5jyefigooLS3A4YAJE/IZOxbM5gLG\njoWbb84nOxsqKwswm0++/rRpQ1P+J598MjDeD4sXQ0MDBatXQ3s7+ZMng8VCwbZtKp+WBlYrBfv3\nq3xUlMpXVKi8x6Pyzc0QHk7+zJmQm0tBWBhccQX5f/0rjBlDwfr1J9+/pGT43xdZWXDrrRSUlsJj\nj5H/1a8OSf2vW7eOeqeThHnzONzezkfr1nHMbqdu6lRqnU5GHTjAeJOJS/LzuSoxkSXl5YwND+fK\nSy4ZkvL1934oKCigvLycM8HvXvpCiIdQJv17hRB/BNZKKV8VQlwNfE5KeYsxhv9TYww/FNgPzEX1\n6PcCy6WUJ4QQvwYKpZQv9HIfbdL3MwXa0cnvBEodu1xqvvrBg6qHfvx4V2/9+HE1zDtmDIwbp9LY\nsV3r3nzTmCqLAAAgAElEQVRSUmB0IHtj2OrZZlOe4Js3q3CumzereLRxcSqUa3T0wJc9tw3CPO3B\npN86llKZ7e+7T0Wzu//+bh79XvN5sc2G3ePB+273vuFPWp5if4fHQ4nN1tlbP2yzEREUxJSICKZE\nRDDZWE4xzPDBgfrD7UGgeelfB3wDCAWeAj4AHgOOApnA/VLKOuPYe1Ae+vHAe1LKd4ztM4FvGefE\no7z0Pb3cSwu+RnOGNDfD1q1d3u/btysfrenTTxbycePUGHvQMAzzjii83uBeYd+yRZnap06Fiy5S\n6cILVYWeT1RWwte/jqyqouGFFzgycSKH29s5YrNxxFiW2GwkhoaSZTYTYfzQvKrmNZ135nsue9kf\nLAQZ4eHdBD5+JMQCOAUBJfhDiRZ8jWZgSKkc43yD05SXK0dl79S2Cy5Qzs6a08DhgF27ugu806lE\n3Svuc+cO/tfYApw2t5tim43DbW0c2bKFI3v2cGTWLI4kJCCByWYzkyIimOSzzI6IIFJ7Z54SLfga\nvxEo5uZzFSnhnXcKuOyy/EGNMNrRoXRo06auOexCdJ+7npc3MoKfDRaD8luurlai7hX43btVABpf\ngc/IOPW4hts94qcedHg8lNpsFPmkbRs2UDd1KvVOJ1khIUwqLGTS0aNMuuYaJk2ZwiSzmaTQ0BHh\n7BaoBISXvkajGRh2u/qK5jvvqFRXp8bPg4K6hmmjorrWe0u97W9o6Oq979ihIpwuXAif/az6Jkh6\neuCOrwcUbrea3nXokHJo8F16PMoUctFF8ItfqChsAwkKUFWl4rGvXUvjtm1UORxMCQ0lZPLkrih1\nubkqyE0ATVdwejyU2+1dom54rhfZbFQ5HIwLDyfbbCbbbGZqRAQZKSl8Pi+Pca+9RvDdd6uvzz34\nYODEyz8P0T18jWaIqa5WX9F8+2313s/LU2G5r75aveNBWYet1t5Ta2vf+7wpJkbpkNc8f8pPk57v\n2GwqCH9PUS8qUt6HOTldH3H3rqemDqzV1NCggsOsXUvT1q1sSE6m4LLLWDdlCqUREYwymaiy28lz\nOpl/4gTzDh1i/ubNZGzZghg1qnsjICdHpQF+ce10cUvJUa+o+wh6kc3GMbud0SZTp6hPiojoXE8P\nDye0p1NHTY0KalNSohz05szxS5nPZ7RJX6MJMKRUJvW331a9+JISuOwyJfKXX64+l60ZIurrTxb1\ngweVOGVmdhd078fcT/dLOxYLbNgAa9fSsnkzH0dGsu7yy1k3dSpFERFcGBdHfnw8S+LimBsdTWhQ\nEC0uFzusVj6xWPjEamW71Uq728384GDmt7Qwv7yceTt3krJrlypvTEz3uPW5uWo4ITX1lN6Ubimp\n8OmpF/v02MvtdlLCwjqFPNtH1DPMZkz9XdvlUkFuiovVd+Uffxxuuw1+8pOAm0EwXDhcDrZXbaew\nthCb04bD7cDusuNwqaXdZe/cdtJ6L8fU31evBV/jH/QY/sBpb4c1a7pM9VFRXb34hQv7Hi/XdTwI\neDxKeHwF3ZtcLsjJoSAujvwlS7oEvo948AOivV2N4a9di2XTJjYKwboVKyiYPp1D0dEsiI1VAh8f\nz7zo6AGHVK1yONju2wiwWIgPDWV+dDTz3G7mV1cz++BBorxBdoqKVGNj3Dg86ekcz8mhKDubojFj\nKE5IoCgigiIpKXM4SAwJ6RTzLK+4m81kms2Y+/MnsNuVx6c3klJxcdf6sWPqk7CZmZCVRcHs2eTf\ncceZ1ekg4vGokZnh8FFxuBx8UvkJ64+up6C8gG2V25iSNIVZo2YRERpBeEg44SHhmIJNXeshpj63\n+W43hZhIjUrVY/gazXBw/HiXqX7DBmXBvPpqFQ580qThLt0w4nQqM0do6OA6DnR0KJHzirlX3A8f\nVlMMvObvvDz40pfUutcMX1AAZ9qwamrqnEtv3bSJTXY765Yvp2DBAvavWMH8mBiWJCTwm7g45sfE\n9N8r7ofRJhOfMZn4TFISoOamF9tsnQ2AfyclsW/2bDIXLmR+dDTxoaEUt7ZSZLVS6nQS53aTbbGQ\nXVtL1qefcuHBg2QfOECmx0Pk6NFq3qU3paer5fjxanjDK+I9hb2mRh2TldWVLr9cLdPTu3+4xidY\nzOnS2KhuWVoKLS2qTWWzdV8OZN1mU8Nj4eHKd+Wuu/zru+IV+ILyAgqOFvBJ5SdMSZpC/oR8vnfB\n97h4/MXEhg/f+Jru4Ws0Z0h9vfok68cfK8e7Y8fgiiu6TPV+GmYNTNrb1dvZKw6+YlFVpQTf7VZT\n0iIiel+eap/JpBzovAJ/7JgSGW8v3ZsmT1Ym78HA4YA9e7Bt307J4cMUnThBUXg4R2bMoDAzk8LY\nWOZGR5OfmMiS+HgWREcTPoQe9x0eD3tbW/nEaqXF5ersrWeZzb1/ga2jQ7VMjx5VczGPHu1K5eVq\njnxwsJpdkJXV2VvvXB8//swtIT1obOz+HQXfZUeHCrOcmanabr4/h57r/e0zm5XYl5TA5z+vfip/\n+tPgfXDJ4XKwrXKbEvjyArZXbScnKYfFExaTn57vd4H3+xi+EOICKeXW0y6Zn9GCr/E3x44pcd+w\nQS0rK9XMq0suUemCCwbtXRiYWCwni7k3NTYqs7ivQHhFYsIE1bt3uVSXq2dXra9tvXXVxo3rGmPP\nyhpUj2+ny0XZ4cMcOXCAoqoqitraOGI2UzRhAidiY0l3u5kUGUl2cjKToqKYEhHB/Ojo/k3gIw23\nW3WBBymqUkND74JeVKR+DtnZ6s/Yc5mSMvg9cZsNvv1t1Uj/97/P7Ns8dpe9qwdfrnrwucm55Kfn\nk5+ez8JxC4e0Bz9ogi+EOCl8rcF0KeXcMymcP9GC73/Op/FlKZWF2CvuH3+sXhiLFilxX7QIZswY\nfIEPiDp2ONRcvo0blfOVV9zb2roLua+wjxkzIuaSS8ML/dUPP8ScnU3RsWMUWa0cCQqiIjqasU1N\nZNvtTAoPJzs1lezsbCbFxzPeZCJEhxbsFSnVzJPCQhVI0Lvcv7+AoKD8PkU9OXl4poa++CLcey/8\n9rdw002nPl5KyeaKzTy942n+c+g/5CbnduvBx5gGyZp0BgzmPHwP8Fe6IhR6GUAVaTQjC5dLedJ7\nxX3jRuVot2iRGur9yU/UOPw5OXe9uVk5nW3cqNLOncosfvHFsHQpfP3r6g09atSIqgCPlJTYbOxs\nbWVHUxM7amrY6XRidjhIXbuWBVu2kB0SwvKkJLKzspg4bRqmtLThLvaAqajoCqS0aZMaYho/vmso\nvufydCcb9EZtra+gd62Hhqoe87RpKhzBqlWqd/+ZzwTeT2bVKuVf87nPqZ/7k092dz3w0mJv4aW9\nL/H0p0/j9Di5fc7tPHnZkyRGjNxpNf318KOklK0+eSGllD23Bwq6h68ZKC0tXZboQ4fUy3LrVvVS\n9O3Bjx073CX1ExUVXeK+caMae583Twn8okVqbGKwBjmHCI+UFNls7LBa2WG1srO+nl3t7cTa7cwu\nLWXOzp3MdjiYk5pK6qxZ6hmzsgJPjfrA5YK9e7tHS7Tbu2ItLFyo2mPez797PwXv+0l4s7n/BkFK\nSpclv7GxZ29drbtcStS94j51qkopI/Cj5RYLfO1r6uf/73+rESkpJZ9WfcrTnz7N64deZ0XmCu6Y\ncwf56fkBGRFw0MfwhRCzgWdRn6t9GbBKKf9zVqX0A1rwNV6k7PLy7S3ZbF2W6Oxs9e6/+OJzdD68\nx6Pe1r4Cb7OpB/amWbNGVFxdt5Qcbm9Xwt7ayo6WFnZbrSTZ7cw+fpw5n37K7NJSZicmkpyXp/7A\nc+dCZORwF33AtLSc/DGjceO6C/zptFekVBaAng0B36XVqu7R1qaCO+XmnizuaWkjpo00IKSE3/8e\nfvFYK1/4xctsdT1Do62R2+fczlfyvkJqVOpwF7Ff/CH4zwCPAl+UUv5KCPG4lPK+syznoKMF3/8E\nxPiygZRw4kTv/mPFxWq/d6yw57DzQAOkDQdnXcd2u5oy5h2X2LxZDZb6Cnx2duBWAErQ6zo6qPZN\nDgeVHR3sbW1lj9VKmtPJ7Joa5uzZw+zNm5kdHEzCzJnKi/LCC08ZOzjQfstlZd3N86Wlqo3iFfgL\nL4SEBP+Wo729uyXgbH8igVTHfbGnZg/P7HiGv+1+BVfxYq4cdTt///kKwkJHhr+GP2LpF0spy4UQ\nXjVtPLOiaTSnhzdwV0nJyam0VL2YfIX8qqu6xD0hIaA1bfBoaVFK4XU+2LVLebFffLGyVz7/vGrh\nBAAOj4caQ7x7inmNT77O6SQ+JIS0sDCVbDbSKirIPXCAL6xfz6yjR4nzivs118DPfhZQMef7or29\n6/fr21AtLOz+MaOvfEWFDhjqkPMREV2hnc9lbE4b/9r/L57e8TQVLRXcNvs2DnxrL+EdY/mf/4FL\nl8MrryhrxrnGQHr4fwHeBy4A1gDXSClvG4KynRa6hz8yaWtT4t2bqFdUdAXu6i2dl/Hhq6u7exYW\nF6uu4KJFATX+XulwsKmlhU0tLWy2WCi12bC63aR6RdybTCbSwsIY5bMtta6O0LVrVajCNWvUVIhl\ny5QD4aJFg9P99BPNzd3F3Nf61NTUfeaidzllihpHD9BHOmc4VH+IZz59hpf2vsT8MfO5Y+4drMxe\nSUhQV7/X7YaHH4ann4a//x2WLBnGAg8Af5j0xwBPANOBPcA9UsrqsyqlH9CCH9hUV6uvh+7apQKh\neUW9uVlZX70vQN+Unn6eh+CWUimFV+A//lipxsKFXQI/e/awf33MLSX729o6BX6TxYLV5eKi2Fgu\njo3lopgYJkdEkBgaSlBvqtbYqL4i5BX4hgYl7suWqZSZGTBq6B0L984n7xmWoKOju5j7LkfIzMUR\nj9vj5ljLMY40HOFIwxGKGovYUb2DksYSvjbra9w25zbS49L7vcaHH8KXv6zm7d9//6CFJRh0/CH4\n10gp3zrrkvkZLfj+ZyBjch6Pevl5xd2bnE7lG5aXpyzOXlEfMyZw/5mGHLebgueeI99m6+rBh4Up\nYfd60OfmDnuFtbndfGKxdIr7VouF5NBQFhoCv9AQ+D69mtvb1fN5Bb6oSDVili2D5ctVgAM/P2N/\nv2WvqHsDxPgGiykqUkXznVPuK+r+CBgzUvHnGL6UkurWaiXoDUVK3BvVellzGckRyUxKnMSkxElk\nJ2STk5zD0olLCQseeOP4+HG44QYV6e+vf/W/D8WZ4I8x/J8IIRYBf5NS7jmNggjgHWArEAZkAl8F\nfgAs9jn0YSnlR8Y59wLRQDywWkr5trE9D7gLKANSUFYG90DLovEPHR3KAdxX3PfsUf8gs2apdMcd\najlunH4RnoQ3uo9X+NavV+b4yy+Ha6+FX/9a2XqHmWqved4Q+f1tbcyIimJhTAy3p6XxlylTSOnP\nyuB0KjfzNWvgo49UUJ9Zs5TAP/kkLFgw5FaKnj31nsIuhBJzr7BfeWXX+kibzSGlxOayYXVYae1o\nxdphxeqw9rps7WglLjyOaSnTmJYyjfS4dILE8DUwG22NXT31hiKONKr14sZiIkIjOgV9UuIkbhl3\nC9kJ2WQmZBIRevY+HWPHqs8B/OAHat7+v/6lZq+eCrtdGa18U0ND97zb3T16cWbm0ITiHkgPPxco\nRwXcmQmsk1L++5QXVoL/QynlI0b+P8C/gGwp5c96OX4B8FMp5ZVCiGDgIDAHaAX2AsuklLVCiCeA\nA1LK53ucr3v4fsLtcbO9/ADF+6NpLJvA7t2i0zQ/cWKXuOflqTTSXohDytGjSvjWrlUpLKzLdL10\nqXJaGEaklJTa7axvbmZDczMft7TQ5HJxUUxMZw9+bs9wsh6P+qhKWZmKx15W1n29slJZJrzPuWjR\n4ESBOQUejwrj35t/SHGxOsa3p+67HuhOnw6Xg9KmUoobiyluLKaosYgqa1Wvgt7a0UpocCjRYdFE\nm6KJDosmKiyqc73n9gZbA4W1hRTWFtJoayQnOUc1AJKnMTVlKtNSpjEmesygzUtvtjdT1FBEUWNR\n19JYd0t3t5667/pQhrB97TW4807VgYmK6l3EvdtcLvUOTEjoPXnfj76+S8XFKvhPX8NBfVmO/GHS\nnwYcAb4EfBOwSCmXDbim1DVCUD39rwNXA07AAQQDv5dS2oQQvwDsUsqHjXPeRM3/PwB8IKXMMrZ/\nFrhJSnl9j3towR8krA4rG0q28erqCjasD+HYrkw81TMJHVVE0Og9TJ3RwdILEvji0qnMGj85IANS\nBAy1tV3j02vXqsnOS5d2jVFnZAxr8aQxp319SwsbmptZ39yMB1gcF8fi2FgWxcWRYzYT1Nh4spB7\n148eVR+rmThRpfT07uvjx/vNGcNuV0U4SdBL3ZTXNBEzqp5RGfUkjqsnZlQ94Yn1RMS2cWnOAq6e\nnk+0yf8NjzPF7rJT0ljSTdS96zWtNYyPHU92YjZZ8VlkJWQxJmYMMaYYJeY9RDw0+MziLLTYWzhQ\nd6CzAbC/bj+FtYXYXXampUxjavLUTmvAtJRpJEcm93odq8Paq6AXNRZhd9nJTsgmOzFbLX3WkyKS\nAub9UlSkwvFGRnYJd2+CHhl5+o1FKdWrojeHz5ISFe26Z0MgKwuWLh18wd8NxKI89f9PSnngdB5E\nCLEC+B6wVUr5M8NiUGaI/J3AHCnlrUKIp4GDUsrfGee9BBQA+4E/SilnGduXAw9KKRf1uI8W/DNA\nSsmxlmNsKNvMm+uOs/njcE7sm4o4fgEpE+u5aJGDL16dwhVLY9m+vYD0vHTWl6+n4Kj6eES7s119\nOGKC+njElKQpAfMPOhh0uDuoaa2h2lpNlbWK6la19F2vtlbjcDu4YeoNfD37i8w50orwivyxYyp0\nn7cHP23asM4P9xgOdhtaWjp78aagICXwhshn1tcjvOb3vXuVooaGniTm7nHpOEZPxD4qHUdwBHa7\nejE5HJy07vGol5o3Qe/rfeVdHhe1jmMUV9dSUl1PRUM9NZZ6Wj31RCbXE55QT3B0PS5TPXZRT7un\nmVhTLEmRSSRFGMmslqYQE++sfoeimCLmpM1hReYKVmSuYHba7CE3X3e4OzrN1T2FvbatlvS4dLIS\nsshOyCYrQQl7dmI242PHd/MuH2rq2uo6xX9/7X4K61SDIDQolGkp08hNzqVkZwmtY1opaijC2mHt\nfI5u4p6YTWpk6jn1zvAHzc29NwQ2bBj8MfwjwK1SSsuZFFRKuRpYLYT4ixDiTinlH312rwPuNdZr\nUeP3XmJQ0f16217b271WrVpFeno6AHFxceTl5XW+PAuMbzOf7/mLL7mY3TW7eeH1F/lkfz1FVVOw\nFV2EuzSO2EQzyy9fwA1PJBEWsomoKHW+x+Hhg1fep7C8kPz8fNLz0pnQPIFbZt7S2QD4xzv/4Gc1\nP0OmS/LT8xldP5q8UXl8+TNfRggxrM/vkR4+XPMhTo+TuRfNxe6ys37tehx1DnLH5lI3oY6Cjwto\ntDUSmhlKlbWKop1F1LfXYxtjIyUyhaiqKJIikpg+fzqjo0eTWJPA1I40rplwAym1bWxa/RFtz/yH\nnKpn+WRiJJ9Onkb6V7/Mld/8LoSEqPI0NJBvvNj6Kq+XwXr+RYsXs7e1lefef5/dbW0cys4mLiSE\nSUeOMDMqisevuIL0jg4Kfv972LGDzIMHcZ1o4OXE6ex2zuNE2D0UpWVQYdmFsxwoz8f+X7DbC/B4\nwGzOxWQCIQoIC4PY2HxMJujoKCA0FFJTVb65WZUnOTkfIaC+XuVTUlS+rq4Aj+ggcux42kzFVNf9\nF1toJTLDjjWsmLbjRwnzxJOQMZGkcUlEh7nInBLLwqWzSInKoqawhlhTLMuXLicpIom92/YSHBTc\nZ/0k7Elg8tTJyHTJ6pLVXP/Y9TTbm7ni0iu4LPMyoqqiSI5MHtTfo91lJ25KHDurd/Lu6ncpaizi\neMJxJsRNIL4mnjHRY1i6ZCmfy/0c9QfqSYlMYdnSZV3Xa4f8+YNXnrPJ79++H4Bv5n+zc79Ml0ya\nM4n9dft5879vEtMYw/033U92QjZHdhxBCNHteu4WN6MmjAqI5wn0/O7dKp+aCgcPFuDxlDNxovq4\n1+kwkB5+MDAVSEaJf6WU0nPKCwuRA0yUUr5n5B8CIgHpjdQnhLga+JaUckWPMfxQVM9+LmBFjeEv\nl1KeEEL8GiiUUr7Q437nTA+/w+PhE4uFJpeLlYmJBJ9h69cjPVRbq9lXu4+NRzfx0fZj7N4Sj6ni\nChzFC4mL97BkqeTay2NYvEgS027HVmTDdsRGe1F757qj2kH4uHCcjU5Ck0OJXxZP/LJ44vLjCE3o\nbiosby6nLwvAcvNUsraXIKqrO7t+0m7HZW/H1WbFZW/HbWvHY2vH47CprqHdDh0dCEcHQY4Ogp0u\ngjtcBLvcWKNCqY8zURcbQk1sMNXRgsoYwfEoDxVRLmqDQgmxJJDUmMy4lnGMaR7D6KbRpDalktiU\nSFtUG06TkxARQum1pdivtZOanMro6NGkRaUxhhgST1gIPnpMDbiVliozdmmp6vVGRSmT/MSJ6ss6\nixfjufAC1lVv4dldz/J+0ftcPflqbpt9G4vGLxqSXkyb283u1lY2Gz34TRYLo8LCWBwbyyVGL36M\nELBtG65312J7fze2Q1ZqYhdQ7ppOtWUsMcFhJHvsBJmDCTYLor6RTuwNozBHBWEyKet8eLiaHn+6\nj9TW0UZJU5eZuqSxhOKmLjP1hNgJZCVkkRmf2dmjzUrIIj0uHVOIf+doVrRU8GHph6wuWc1HpR+R\nGpXKigzV+79kwiVEhg08NG+LvYXdNbvZWb2TnTU72VW9i9KmUnKSc5g9ajaz01Sanjp9UBzMNOcn\n/hjDvxdYCVQALwBXDCS0rhAiA/hfYCcQCkwBvmOkCFQvfTrwEyllsXHOPSgP/XjgPSnlO8b2mcC3\ngKPGvnt6NjpGsuDbGzvYWdjAvoNNVBRZsZXZyagNItIisUbChNRIstOiMCWEEhofSkh8iEpxIdgi\nbFQHVXNUHqXUWUpZcxmHq2ooLnFTVWHCZJlMRMPFtB+5gPDQUJZeCIuz3cyLaSW+oZX2I0rY7Uft\nmNJMmLPNmLPNREyK6FwPTw8nKDQI6Za07mmlaW0TzWuaadnUgjnbTPzSeOKWxRG3KI7gSB9nLreb\n6rVvUfvqi8Su2UR8dRPrs0OpTo2gFSdW0YFFOPGEhYDJhAg3ExRuJtgcQbA5ghBzFCERkYSZowmL\njMEUGYMpIobwqDjMETHENruIOdJK1BEL5vJGTJUNhNU1ENZcS2h7PWGeeoTw4IpIwRM/Cpmahpgw\nhuBJ4wnJHU9Q+lhkYiJtq4to+ctuPIdLiJ/YRITpBEEVZSoq0MSJXaLec3kKx7P69npe2vMSf975\nZ9zSza2zbuWWvFtIiRycL43Y3G72tLbyqdXamUrtNsYFuxkrWpke4mZOcxDJJ8KI3tWKeXsDQUUd\nuOrCsDEal4ygMQiqzXGEpkeRNiuSnGVm0maHEz4xnJCoECzbLJTcX4LzhJNxD48j7PIw2p3ttDnb\naO1opa3DWDrbuq1793nXKywVFDcW02xvJiM+Qwm5MfacmaDEfbjN1L64PW521exidclqPij5gJ3V\nO5k/Zj4rMlZwWdZlzEid0Wn+r2urY1fNLiXu1TvZVbOLams1M1JndAr77LTZ5Cbnnta0MI3mVPhD\n8H8upfypEOJ+KeVjQogfSikfPeuSDjKBLPjuNjf2cju2Mhv2Mju2Mjs1RVYspTaCK5xIl6RxjCBo\ngomEzAjSJ8WSmBVJSGIIOyoaebOoisZGJ1Pb2khurKe9roPa2ggam2Ox2pKwOBJpdMZywmOmRphx\nIhhtcjA2ysm4eDeZkXZmtNaTdLyF0ISQboLuXYZnhBMc3n9UkIIe48ueDg+WTyw0r2mmaW0T1h1W\n4qZLRo3ZS5x1E6G71iJSUmDlSjWv6aKLONZeTbuzvdOZKDIsss+XvJSSjpoOVWelqu68yVZmo6O6\nA9NoE+EZ4ZgzzIRPDO9azwgnNDEU0dqqXLWrqpS3eM/1ujoYPRomTqQjdhwN+2Oo3RZJxMpppP0o\nj6jpZx+1TkrJluNb+PPOP/PGwTdYnrGc22bfxqWZl540Ztyzjr04PB729hD3I+3tpAU7ie2oIbjq\nMNGflJFRFMG82tmMPT6KiPooRIiFSHclwUE1VCQ0syOpmY+zmihPP0FrYi0yzE6Hx47D5cDlcREW\nHEZ4SDimEBPhIeG4PW7aOtrI2Z/DrR/eiiPcwatXvUrllEr19wuN7Pw7dq6HRhIZ1n19bMxYMuMz\nGRMzZlineXnpq577wuqwUlBewOqS1awuXU2zvZmZqTM5VH8Ii8PCrLRZ3XrukxInERx0fkfZOd06\n1pw+/hD8h6WUP/IR/EeklA+cdUkHmeEWfCkljuMOLFsttO5sVQJVrsTJ3eqGcWE0jQmiLNnNnkQn\nHeNCmDgphllTE1g0MZEUk4kTrSfYXrWdbcd2sGFfKfsPtNNcHUdU+3SC2mbS3pyNoy6OoNYwklLs\npI9zkz7ew+jRHYwe7SA1uZ3kqFYiZDvOlg46WjpwtDjIHJPJxAUTMWeZCYk6wx6U1UrBxx+Tv3Jl\nzwdXk/HffRf51juwaxftafOod87nROMcQhdOpm2hmUNzg9g4voMdtjZChGCCycSE8HAyHKFMqA1i\nVJUkttJD8FFnZ73Zj9oJjgpWQj7RR9QnhmOeaMY03kSQHz5y4WxwUvV0FZX/V0nkzEjG3T2O+OXx\ng2KSb7G38I/Cf/DnnX+mob2Br838Cl9LW8noegeUlVGwaRMXjR1LYUgIn0ZE8GlUFJ/GxXIoOob0\nxjqmHCth8pGD5OxqIuNoDCbbZJyOSbjcSUSFlBETXESU+wCm4EoOxOfyessS9qRcSualGeQvESxe\nrNo3veGRHhwuBw63A7vLjt1lJ1gEdwp6KKGc+PsJyn5SRlReFBmPZBA5deR8gc6XsxWj8uZyCmsL\nyXwPNV4AACAASURBVE3OZWLcRO101gta8P2PX3r4wAK6zPA7vVPnAomhFnxXqwvrp1as26xYtlmw\nbLUg3ZKYC2KInhNNw7ggdic4KIi18X5wCwlhYSyJi2NJXBwXR8XReNzBB9sPs25LGYX7WjlxLBxn\n81iELR1PRyqIWoLEUYKDKwgOPkZISAWhoccJDj1Oe1ANduEhOjSURJMJU0gIwcHBvaagoCAOHz7M\nK6+8wpL+AkO3tHRNsSov70revM2mBmyDg9VccbNZja/X1KjB3HnzcF16KftWrGB7XByftrdTWGnB\nvLmd/H0hzNghiWrwYLo4BoLBXmqHox1It6RldBA1aVCe6uH4KHCPDyVsYjixE82MSYzobBxMCA9n\ndFgYIUG9i7zL48HidmNxuWhxu2lxuWhxubD4rLcY+yzGus3jIdtsZnpUFDMiI5keGUmc8alYj8PD\niZdPUPHrCkSwYNz3x5HypRSCwk6jkeGN8OI7lc1I9uLDNLVY2DwpnZ3TcynLzePw+AwORMcwurWJ\ncfVHiavcT9LBCqZWJTPOOoO4+ixCahMIHwPx00KJnhFGyBQzu5sj+WiLmQ8KTHQEhbPosgjylwax\neLGKZjiYuO1uqp6q4tivjpF4dSLpP0snfGz44N5Eo9GckkEXfOOilwEzgN1Syg/Ponx+w5+CLz2S\n9kPtWLZaOsXdVmwjakYUMRfEEDYvktJpQWyLtbPFYmFzowVTo5np1kTS6iJwHHFweH8T5UehuSEe\nlz0ZRC14ygkxVRCX0MyECTAzN5a8vDjmzUtjypQM4voJvVTtcPDb48d5rrqaqxITuX/8eHL7+N73\nurVr+dKXvsQvb7+dW2fN6l3UnU415cqbJkzoWo+PB4tFfbfzrbdg82ZkVhYncnPZMmUKa0aPZnt0\nNIUJCUw8cYJ5Bw4wt7KSuRYLM4HwUaNg9GgckeNprh2NyEwnfNYowicaZnef3pHV5eKYw8FRu70r\n+eTrnE7SwsIYZzLhkvIk8Y4ODiY2JKQzxfjkfddjg4OJCQnBFBREUXs7e9va2Nvayv72duJDQpgR\nGckMoxEwLTKSlI/tVP+2krb9bYz55hhG3z66y2HRYul9jro3HxKCPTubg7NmsTcnh31jx7IvLo59\nYWG0CcHUCDPhjiqOVhbQfmgXy09ksKB2FulH04k6FIUpwUTM/Bhi5scQPT+aqFnRHCgN5v334f33\nVeC6Cy9UAfquuEJ9jGUoOpzOZicVj1dQ9UwVabemMf4H4wmNP7P53hqN5vTxi+D3uMENUsp/nnbJ\n/MxgCn5HXUensFu3WbFstyATw3DOiMeeGcvRFBO7giSFNS5Kqt00VDoJr4WghmCcFjMdjihCRB2S\nMtyeUkJDy4mJqmJ0UjO56bAoL5WLp88mOyMTc1yccnsODVVfmDlwoCtebWWlCrGUlKSiPMTGqtCr\nkZHqnJAQmhwOnoqJ4f+NGcNFtbX8YPt2Fvx/9s47PK7qzP+fI2lmVEayZPUuVxkj23LHxhgRUwIY\nU8KPTRY2EMIuJLuwQAzZUEwLGyCU1E2FhJBdQkhxbIoNNjZgcO+9SlaxVW1JozL9/f1xR+ORLGHJ\n0kgj6Xye5zz3nHPv3PvO0dV8T33P0aOGg5e2UFPDYY+HhS4X12Vl8fzVVxPetqY6L8+4d1sLv2Mo\nLkY8Hhw5Ofw9ORnnTTfxVmEhnypFutnMjNhYZsbGMiM2lqlWK9aICMNvZFXVmXHywGN5ubFfe3q6\nsS79ssugqKjb7vmcXi/lDgdlDgdmpdoJuTU8vNddq14Riu12djU1sdtXCdhls1HucJDv8TB/ZxOX\nvOUlcWcMCYnbGd/0e6I9Zf716d68PEry89mdl8fupCR2RUay2+mk6lQrhTYLU5simdBoIud0GMl1\nCku1B+cJJ46TDpwnnOw07eTSiy8ldlasIfAzYzEnm6mvNzb0WLHCCJGRhrhffbVRfF3U9foFR4WD\nkidLqF1aS/bD2WTem3nO+SADje5uDj66jINPnwm+Uqq4i8/EiUjIOU89X8EXEUp3lPOPXx9lx5pI\nWssTsDmiqIoWakxhnPZYaLZb8bjMqCgbEtmIUjVEOMsId5ThcpRhkSpSVTXJlmoSYk+RmNjIhQmx\nFCakUhiXRmp4LOEu9xkvJHa7setZQ4MhyC0txjmljCBieCpRyugub1sDFR5unHO7DUf2drvRtT5i\nBO6EBPZnZLAyKwtvYiILUlOZlpODGjvWqDA0NNC0dy+/e+IJsjweFl54IabycigpQZxOHDk5NGRn\nU5WRwfG0NA6kpLAzKYmNI0dywmolLyqKpL17uWbBAmbExjLNaiXBdJ6tOY/HcLy/Zo0R1q0zZr63\nVQDmz+/fvW/r68/u9QgMLhfN+fnsC2ihH/MmkPeOmcvfhYrpJipuiqam0UlzhZ30U4pR9RGk1ini\nar2YqjyECVgyLZgzzFgyfMf09mlzupl1W9YZvgO8Rp2vrRW/c6fhkbatFT92bOi5fm3e30zxI8XY\nttrIezqPtH9JQ4WHmJE+tBgFH13GwacvBf/bIvI/3c0faHoi+MU7yvnr/xSz70M3UaXVJHsPMTvs\ncyapXbSER1ATYaEyLIITeDjpbKLG3UhzlBARFUlSTDQZGelk5uczpnAq4+bMJWHyFEOUO8PlMlrt\nW7fCtm1G2LXLmDk1bZoRpk83nNEHbsfk9Roh4gsm2bndZ7WkPeXllBw9SnVJCWk1NWTV1hLh9eLI\nyaExK4vKtDQ+3LOHnVVVOB9+mO3jxlHmE/S8yMizwqjISJJMpuBOSnK5jFb/Rx8ZFYANGwzf65dd\nZlQC5s3rXRO2sfGsXot2abe7/XBGx9CFY3URoeJUK/t/W47rnXqik80kZUcRlxVliHi62S/o4bHn\n7n2orjac861YAStXGnWeq682RP7SS4263WCg4fMGjj58FHe9m9HPjSbx2kQ9qU2jCQJB79IPVb5I\n8I/srOAvPz5C7QflJJw8Tq53H7PYQAYV7I4YyXqa2RjWys7cLEbGJzLJbGaa2UxhdDQTYmKIM5lQ\nDQ3GEq7qaiN4vUZ3e0oKJCefiaekGOK/a5ch7vv2GaLRJu7TphniHhcX1PLwirCstpbnSkvZ2dRE\nbpuAR0WRa7Gw7/XXWfHLX/L7t97i6nnzQusH2W6HjRvPVAC2bTN25WmrAMyZ076C1dRktNADhTww\nbrefcQvbFgLTA7RTSnW1sUHe2rVGqKgwWvFtIj/AbvZ7hYhQ904dx/7rGKZEEzmP5DDyypGosBB6\nzzSaQY4WfODA9hO8//11tKzeS1pDKQXspYDdHDPFsiEaNmW42DYukuJRkUTEK4h00uQ5DQhrbl/D\n7KzZ535gc3P7CkBgaGkxfKZPmwZTpgzsACvGj29ngv7OO+9w55138pOf/ISvfvWr57zPgHXRtbQY\nEwbXrDEqAXv2GJUmh7GUjaamzoW8LZ6UFBL9350J/Lx5xhh8UZFRp1m3bmh1g3rdXqr/t5ryn5Tj\nPuUm/d/SSb8zHXPqwDqg0d3NndPU1ERkZCQRX9Sz2E10GQefngp+aLi16iNeTp9PQesJprdU8JUI\nYWNqBJsnu3ljlJOdGSYi4yIZnTKWC5LHcsOIbLLisvwhMy6TD45+wG1/v43td2/Haj7HLloxMUbw\n+e4PZbpqvS9cuJBVq1axaNEiDhw4wBNPPBFaLf02oqPhiiuMAEYX/aZNhqe7vDzDwXQI2v1FAv+N\nbxgC3we/qyFNWEQYabenkXZ7Go1bGjnxyxNsmrCJhCsSyLgng/jL4kPznRtmlJaW8sorr/Dqq69S\nUFDAihUriAtyL6Sm/+nOOvwZIrIlIH2diCwPumU9RCklzxWksDMhjh2xo6h0fQlVP5MYVzZxZBJj\njiEqytCOwGNgPCEBPk/5BtaoCH6z6DcD/ZX6jaqqKm644Qby8vJ47bXXiBosg8UhRkeBLy83uugD\nW/BDXeC7g7vBTdUfqzjxyxN4HV4y7s4g7Y40TIl6SV9/s3PnTn74wx/y/vvvc+edd3Lffffx3HPP\nsW3bNlasWMGI/pw8q+kxwXC88wlwk4jU+ja4+bOI5PbSzj5HKSVO5ykiIhKw2w0/MS0txjEw3vEY\nGD9+HJavtME9hbxyzYvcMfvGgf5a/YbdbufOO+/k2LFjLF26lLS0tIE2KaSpqTFmzreFLVvOjMFr\nge8eIkLjeqPVX7uslqTrkki/O50RF4/Qrf4gIiJ89NFHvPDCC+zevZv//M//5O677/b7/RAR7rvv\nPjZv3szKlSu16IcwwRD8m4FpGN3/l2FsavNEr6wMAkopOXDgLvLze9cyLy2F+19az1LLjdwTto2n\nvpNBcnIfGRniiAjPPPMMr776KsuXL2fy5Mntzg/HMTm3Gw4dai/uO3calcTJk40pGlOmGFMKpkzp\nvcAPxzIGw51x5R8qOfHLEyiTIuOeDFJvS8UUH5xW/3AsZ7fbzV/+8hdeeOEF7HY7ixcv5tZbb8Vi\nOXsXQhHh/vvvZ8OGDaxcufILnYB1xXAs4/4mGGP4EcAFGK51XwdWnKdtQefUqRXU139MfPyl532P\nnBz424/ncP8/7uZvG7/Bm/nv82//GsbixQx54VdKsWTJEvLz81mwYAGvvfYa1113XZ/dv7a2lv37\n93PhhRcyMnAJYg8Q8fsSIiys/bDM+boFaOP0aWNxRaCw79tnrKBsE/Z77jGOubkhOW1g0GJKNJH9\nQDZZ92dR/3E9J355gpLHS0i6KYmMezKInRGrW/3nSXNzM6+99hovv/wyWVlZPPXUU1x77bWEdeGi\nGozfgh/96Ec88MADXHHFFXzwwQckJCT0o9WaYNCdFn4j8G0R+aNSag7wExGZ2S/W9QCllFRX/51j\nx/6LGTN2EB7eO9/ebq+bea/N4+qsf6Z6+X28+SbcdRcsXmysvBvqbNy4kZtuuonvfOc7PPDAAz36\nsbXZbOzbt4/du3ezZ88ef7Db7YwfP55jx47xH//xHzzwwAOMGDECEUNsq6rODtXVZ+dFRBiVL5H2\nQzTQ9fyMruJhYXDggCHudXUwadIZcZ8yxUjH9n7DPM154Kx2Uvm7Sk786gQR8RGk/2s6kXmRoDCW\n94X5JqSG+dKKdnH/NR3OhceEEzVm6M9Tqamp4Wc/+xm/+MUvmDdvHg899BBz5szp0T1EhAcffJBP\nP/2UDz/8UIt+PyMewXHSgeO4A/txuz+0pWfvn93nXfp3ishrAekbReTvvfgOQaFtWd6ePTcREzOJ\nUaOe6vU9j5w6wpxX57D29rXEOS7kuefgzTfhm9+Ehx4a+sJfWlrKddddx6xZs/j5z3+O2dx+KZXD\n4eDAgQPtRH3Pnj1UV1dzwQUXUFBQ4A8TJkyivDyDNWsUO3YcY+PGp6mqeo/o6AdoabmXmBgrqal0\nK0RHd26vy9X1/Iyu5m+4XDB+vCHuY8YYFQBNaCFe4fSq01S+Xon7lBvxCoiRjxd/OjDedq7ddWIc\nndVO4mbHMebFMUSP6+JlGsQcOXKEl19+mTfffJNbbrmF73znO4wfP/687yciLF68mLVr1/Lhhx+e\nd++c5my8Di/2MnuXgu6ocGAaacKSayEyN9If2tKxk2ODsnnOIiAO2AEUi0jz+X/F4NAm+A5HBVu2\nFFJY+AkxMRf0+r6vbnuVn2z6CZvu2oQlwkJ5OTz3HPzf/w0P4bfZbNx6663YbDaKiopQSvmFvbi4\nmNGjR/tFfdKkSRQUFDBq1CjCwsLZu9fwHLdqFXzyieFIZsECw4leaiq0th7kjTeeZOPGNTz88MN8\n61vfGvYrBPS4Z/DxOry8fd/bZP41k7Tb08h9PDdocwX6k82bN/PCCy+wdu1a7r77bu69915SU1P7\n5N4iwsMPP8zq1atZtWpVt0R/uL/LIoK73o2j1IG91N7+6BN2V60LS4alS0G3ZFu+cF+KYEzaewFI\nBlzAL4BviMh93X1AfxHoeKei4udUV/+JwsKPUap3TTYR4St//gqjE0bz4pUv+vPLy+H55+F//xfu\nvNMQ/j763wo5PB4PTz31FKtWraKoqMgv7OPHj2834aes7IzAr15tOMO74gq4/HLDSV5XcyD27NnD\nE088wYYNG/je977Hv/7rv3Y6kWg4MNx/JPuLtWvXMveCuRQ/Vkzt8lrynswj/a50wiJCt4vHZrNx\n/PhxfygpKWmXNpvNPPjgg3zzm9/Eaj2HH5HzQET47ne/y4cffsiqVatIPMeGV0P9Xfa6vDgqHF0K\nuqPUAQpDuHMsROb4hDzHl86NxJJh6dV+E8EQ/EdF5Fml1HdF5Hml1H+JyHPdMEQB7wAbADMwBrgT\nY/LfD4BjwDjgERGp9n3mISAWSAA+aFvvr5QqBL4NFAMpwGIR8XR4nl/wRTxs3z6PtLRvkJHxb90s\niq6pballyi+n8Icb/sCC0QvanRtOwt+R+nrD+V2byNfWGi34BQsMke+pa9ht27axZMkSdu/ezWOP\nPcYdd9yBqbcz8TSac2DbYePI/Udw17kZ88oYRl7e/13WIkJdXV2nQt4W7HY7ubm57UJeXp4/npGR\n8YUT8frKzu9973usWLGCVatWkZSUFNTnnQ+uehfNu5pp2tFE004jtBxoAS8ok0KZFGGmMH9cRXSS\n10VavIKj3BB5Z5UTc5r5jJj7RNwfz4kkYkRw1+UGQ/BfEZEHAgT/JRH5TjcMUcD3ROS/femlwJ+B\n+cAqEfmLUmohcIuIfN23xn+JiFyrlAoH9gPTgSZgF7BARKqVUi8C+wLnFfju386XflPTbnbu/BIz\nZuzCYknvbnl0yQdHP+CuZXex454djIw6+wehosIQ/j/+EW67DW65BS66aGitw7bbYf16Q9xXrTJm\nsM+da4j75Zcb4+B98Xuzfv16lixZwrFjx3jiiSe49dZbCQ8P7e1WNYMbEaF2aS1HFx8l5sIYxrwU\nvPF9h8PB9u3b2bhxIxs2bGDXrl2UlJRgNpu/UNCTkpJCYqWCiPDoo4/y7rvvsnr16gETffEK9mK7\nIeoB4u6qdWGdZMVaaCVmSgzWKVZiJsZAOIhbENeZ4HV5z05/wTWEgSXLEHNzhnnAe4SCIfjfAu7F\nmALTCvxKRH7bQ6MiMFr6dwN/B+aISIVSaiRwWEQSlVLPAHYRedb3mX8AvwX2AStFZKwv/0bgNhH5\nSodnnLV5zrFjj9LaepgLL/xzT8ztkvtX3M8J2wneuvmtLv/xKirgV7+CZcuM1v/VV8N118FVV/Xv\njq+9xW6HvXuN2es7dhjHTZvWMmVKkV/g58yBYPa8f/zxxzz++ONUV1fz5JNPcsstt/RJC8bj8XDi\nxAlKSkqoqqpi8uTJjBs3LiR+TId6N2io0FU5ex1eyn9STunzpX0yvi8iFBcXs2HDBr/A79mzh/Hj\nxzN79mwuuugipk6dyqhRowaVK1sR4bHHHmP58uWsXr2a5E7G6/ryXfa0eGje3ewX9aadTTTvaiYi\nPsIQdJ+wWwutRI2JGjabNAVl8xyl1AVAAbBbRA700KArgQeADSLylFLKDqSISKOvIuAETMDPgf0i\n8mPf594A1gJ7gV+IyFRf/uXAEyJySYfnnCX4Hk8rW7ZMZsyYV0hKWtgTszul1dXKzN/M5OGLH+br\nU75+zutLS+Gdd4ywbh3MmmWI/8KFxozwUKGq6sy68zZxP3oUxo0zWu2FhcbRbl/LwoVF/WqbiLBq\n1Soef/xxWlpaeOqpp7jhhhu+UJw9Hg8VFRWUlJS0C23dpeXl5SQlJflbTTt37qS1tZWLL76YefPm\nMW/ePKZOnXrWqoT+QAt+/3CucnZWOSl+vJjaf/jG9/+1e+P7DQ0NbN682S/wGzduJCIigosuusgf\npk+fTswAb6jVF4gIS5YsYenSpaxevZqUDrOXe/Iu+5eflTtwlJ052kvtNO9pxlHqIDo/2hD2Qqsh\n7pOtw94dc9B3y1NK3SMivzwPw14HNgL/BcwVkfIOLfynAaeIfN93/T+A32C08D8IaOHfBNzaWQv/\n9ttvJ8+3mU18fDyFhYVMmeLhwIE7aWn5JeHhUf4XcO3atQA9TidMSODyNy7nJxN+Qnpserc///77\na9m6FYqLi3j3XbBY1jJ3Lvz7vxcxZw58+un52dOTtMcD6elF7NwJy5ev5cgRKCsrwuGAnJy1jB0L\nCxcWMWUK1NSsxWwOrj09Sa9Zs4YNGzbw9ttvo5TixhtvxGq1kpCQQElJCevXr6eqqoqGhgYqKiqI\ni4sjLS2NKVOmkJubi8PhIC0tjeuvv57s7Gw2bNjQ7v5vvfUWe/bs4fTp06xbt46DBw+Sn5/PwoUL\nufjii/F4PFit1pApD53un/T0+OkcfeAo60vWk/nvmSxavMh/3uPxkJyczIYNG1i6dCn79u2jtraW\nqVOnkpGRwcSJE7nzzjvJysri448/Donv09fpSy+9lCeffJI//OEPvPzyy9x4441nXS8e4cO/fYiz\nxsms5Fk4yh18sv4TnNVOpjin4ChzsPHkRiLiIpgzdg6WLAs71A5MySaKioqImRjDpqpNhJnCumWf\n1+vlb3/7G9XV1SQlJVFWVsbmzZuxWq3MmTOHtLQ0ysvLGTlyJNdffz1mszlkyvNc6bZ4SUkJAK+/\n/nrfCL5S6hTQgNH6HgnUYMzWbxCRcw6K+3oFRonIe770k0CML6wRkbeVUtcBN4vI7R3G8E0YLfsZ\ngA1jDP9yEalSSr0E7BGR33V43lkt/Db2778DkymBsWNfOZfZ3eKlz1/i7wf+zto71hIR1vNBeq8X\nNm82Wv7LlxvDAIFd/+fTs2e3G45jamuNY2AoLu7ca1xbyz07e/B4jfN6vSxdupQXX3yR8PBw/xhn\nXl6eP2RnZ/d6ln9DQwMbNmxg3bp1rFu3js2bNzNmzJh2vQA5OTl99K00HbHZbFRUVFBRUcGJEyeo\nqKigqqqK1NRU8vPzyc/PZ8yYMf2ymsPr9bL393v56LGPqEiooOqCKg6WH2Tv3r1kZGRw0UUX+bvn\nJ02aNCwmmopXcJ1y4ap24apx8ezPnmXZumW8cesbxLfE46pxGTPYy4zJbaZEE5ZsC5Ysy5ljYDzD\nQpi5e8N1DQ0NlJaWUlpaSllZ2VnxEydOkJCQQE5ODtnZ2eTk5JCamkp9fT1VVVVUVVVRWVlJVVUV\nNTU1WK1W0tLSSE1NJTU1tct4SkrKgPT6fRF91sJXSt0qIv+rlLoPeE1EmpRSVuD+tlb4OQwZDfwQ\n2IZRaZgA3IexvO954DjGzP3vikiN7zOLMWboJ2D47H/Hlz8FYx7Bcd+5xSLi7fC8LgXf6axl8+YC\nJk1aTlxc750EesXLlW9cSVFeEY/Nf6zX92vr+l++3Oj6nz3bEP9Zs6Chob14dxT0trTLZWz7nph4\nJrSls7IMce+t17i1w7i72eVysX37dn8F4LPPPsNisfgrADNnziQ5OZmEhATi4uLOe67BUC9jt9tN\nZWWlX8wDBT0w7Xa7yczM9IeMjAxSU1M5efIkhw4d4uDBg5SWlpKVlcX48eP9lYD8/HzGjx9PRkbG\nFw77dFXOtbW1fj8Te/fu9R/Dw8MpmFhArjuXpJ1JzLh2Bl967kukjBoYJxwuj4t9NfvYcmKLEU5u\nwSterhh9BV8e+2XmZs/FHN4zcfK0eHBUOHBWOnHVuHBWG0dXtQtnjdM4tuXVuYgYEYEp2YQ5xYwp\n2cSvS3/N+yXv89YDb5E1JotN1ZtYcN2CHom50+mkvLy8nYB3FHWPx0NOTo4/tIl6WzwrK4vIyO55\nWvV6vZw6dapdJaCreE1NDUlJScyZM4f58+dzySWXMGXKFCIGcGZ2MCbtPSsijwakfygiD/XCxqDw\nRYIPUFn5R8rKXmT69M2EhfW+Bl7eWM70X09n+deWMytzVq/v10ZTkzEDfvlyw697QsLZQh4o5m3B\nag1+K32oi1FPEBGOHDnirwBs376duro66uvraWpqIi4ujvj4eBISEtodO8sLPLd3716uuOKKgf56\n7fB4PDQ3N7cLTU1NPcqrrq6moqKCuro6kpOTycjIaCfmHeMjRpx7xzyn08mxY8f8FYCDBw/64y0t\nLf6KQGCFYPz48VitVt555x1GjhzZTtj37NmDw+Hgwgsv9DuTaosHjk87q5wULymm+s1qrIVWYmfE\n+kPU2L6fMObxejhQe6CduO+q2kXuiFxmZMzwB694WXlkJSuPruRg3UGK8or48pgvc+WYK8lROca4\neIUxPu6scBrpgDxPiwdLhgVzutkv4qYUE+Zks3EMyDMlmggznS3iTz/9NG+++SYfffQRBw8ebPd7\n4fV6qa6u7lTM2451dXWkp6f7xTs7O5vc3Nx2oh4fHz8gE2y9Xi9lZWV89tlnfPLJJ3z66aeUl5cz\nZ84cLrnkEubPn8/MmTO7XdnoC4Ih+H8D1gOHgXyMGfY39MrKIHAuwRcRdu26ioSEK8jJ6Zv6ytt7\n3+bRjx5l293bsJr73tGFZnDi8XhoaGigvr6e06dPtzt2lhd4rr6+ntGjRzNp0iQmT57sP+bk5AT1\nR87hcHDw4MGz3CSfPHkSh8NBdHQ0MTExWK1WYmJizoqfK52SkuJvpfdHi6i+vr5dBaAtfvjwYSIj\nI3E6nUycOPEscc/MzOx2ObtOu2ja1kTj5kZsW2zYtthw17uJnX6mAhA7M5bI3Mhu39MrXo6cOsLm\nis1+cd9RuYM0axozM2b6xX1q2lRiLbGIR3BWO9sJt6PcQeXJSj6xf8K6yHVsSNlAtCuaubVzmeea\nx8XWi0nISMCSZcGcafZ3r5sSTX3yjn3/+9/nj3/8IzfffHM7MW+bW9Mm3p0d09PTB9US3NraWtat\nW8enn37KJ598wv79+5k6daq/B2Du3LlBXX0RDMFPxJhoNxFjAt1zIlLXKyuDwLkEH6C19Shbt85m\n+vTNREWN6pPn3rH0DizhFn513a/65H6a4U3b/gS7d+9m165d7Nq1i927d9Pc3ExBQUG7SkBB1Mz/\nJQAAIABJREFUQUGP9yr3eDwcPXr0LGEvLi5m1KhR7fY/KCgoIDMzk+jo6JBYstgXeL1eamtrSUpK\nCoqTGmeN0y/+ti02bJtteJ1efwUgbmYcsTNiMWeYEYRjp4+x7eQ2f+t968mtjIwayYyMGUxPmc4U\n8xQmOiYSVRV1lqg7yo3u94iECCyZFiNk+44BYm7KMLG3eS8rj65kxZEVbD25ldmZs/ny2C9z1Zir\nKEgp6PO/7+uvv87x48fbCXpWVtaQd51ts9nYsGGDvwdgy5Yt5Ofn+3sA5s2bd9Zqht7QH7P0p4nI\nth5bFmS6I/gApaXPc/r0GiZPfr9PXvJGRyOFvyzklate4foJ1/f6fqGM7tIPPl2VcV1d3VmVgL17\n95KUlNSuEjBp0iTGjx9PeHg4ZWVlZwn7gQMHSEtLO0vY8/Pzh5U74/58lx0nHJzafIrtW7eztWQr\nu5p2cTj5MEdTjhIXEcfkqMkUOAuYUDeBcaXjiD4ejaPcgfuUG3PqmRZ4YGvckuUT9gwLYZaeVVwa\nHY2sKV7DiiMrWHF0BU6Pky+P+TJXjb2Ky0df3qljsfNB/14YFfgtW7b4ewA+//xz0tLSKCwsJCYm\nhsjISCIjI7FYLP54x/BF5/Ly8vq8hT8duB3D5S3AJBGZcf5FEBy6K/her4utW2eQk/NdUlP/uU+e\n/VnpZ3zlz19hxz1G19tQRf8DB5+elLHX6+XYsWPtKgG7du2ioqKCiIgIrFbrWcI+ceLEoPhZ99sk\nXmwOG/X2en9ocDQwIWkC40aGhnMjCO673OxsZlfVLrZXbmf7ye1sr9zOvpp95MbnMi19GoWphRSE\nFTC6dDSmHSYc5Q7MGeYzIt4m8KnmXvlZ7w4iwuFTh1l5ZCUrjq7g0+OfctXYq3j+8ucZndBD39gd\n0L8XZ+PxePyVdbvdjt1ux+Fw+OOdhS86X1pa2ueC/znwMsayPIXh5e6uXn3rINBdwQdobNzEnj3X\nM3PmHkymL94AorssWbOEzSc2894/v9frHzW3101pQykRYRHkjNBLvzQ9o7m5GYfDcV7bmHrFS6Oj\nkQZ7Aw2OBhrsDe3Euy2ctp/uNL/R0Ui0KZr4yHh/iLXEsrNyJ5ERkVwz7hquGXcNl+ZeSpRp8Hfv\nnmo95Rf1NoEvqS9hYvJEpqZNZWr6VKamTWVy6mRizKHvbKfF1cIr61/h5Q0v882p3+TRSx5lROQg\nchE6zAjGGP4vRORbAek0EanshY1BoSeCD3D48H14PE1MmPDauS/uBi6Pi3m/m8e/TP4X/mPWf5zz\nervbzrHTxzh66ihHTh3h6Okzx9KGUtKsaTQ7m/n5NT/nnwr+qU9s1Ax93F43VU1VVDdXG8LtE+1O\nj46Gs8S92dWM1WxlhGUEIyJHtBPueEt8+7QvJEQl+ONxlrhOfVOICLuqdvHe4fd478h77Kzcyfzc\n+Vw77lquHnc1efF5/V9Y58DpcXLSdpIKWwUVjRXtj7YKSupLON16msK0wnbiPjF5Iqbwwb0W/6Tt\nJI999BjvHn6XJ4ue5K5pd52XzxFNcAmG4L8KVAKHfFkLReT/nb+JwaGngu9229i8+UImTPg9CQlf\n6hMbDtcdZu5rc/n4jo+ZmDyRRkcjR08d9Yt5oLDXNNeQG5/LmIQxjB059sxx5BhGxY/CEmFhZ+VO\nFv1pEXcW3smSS5cMeHeo7qI7GxGhtqWW6uZqok3RWM1WrGYrkRHdn5kdSFdlLCLUtdZxwnaCisYK\nTthO+EOF7Uy6pqWGpOgkkqOTGRE5wi/cIywd4l0cYy2xhPVyS+nucKr1FB8e/ZD3jrzH+4ffJzkm\nmWvGGq3/i3Mu7vEa8p4gIrz74buMKhzVpZiXN5ZzuvU0KTEpZMVlkRmXSWasL/jiOSNyGJUwql/K\na6DYfnI7D6x8gNqWWl6+6mWuHHNltz+rfy+CTzAEfwfGhjdgdOlfIiILvuAjA0JPBR+gtnYZR48u\nZsaMXYSH983ayd9u+y3fW/09FIpmV3Ongj525Fiy47IJDzv38pPKpkqu/9P1jEkYw6uLXh3QbtDh\n+A/c6mqlrLGMsoYyShtKz4RG41jWUEaUKYqUmBTsbjtNziZsDhtur9sv/m0h1hJ7Jm3qkPaFA5sP\nEH9B/FlCftJ2kmhTNBmxGWTEZpAZl0mGNaN9OjaD1JjUQde69IqXrSe28u7hd3nv8HscqjvEgtEL\nuGbsNVw97moyYjO6fS+bw2aUV9PJdmV3oulEu7Sn2EPulFwy4zINQe8g5plxmaTGpHbrf3SoIyIs\nPbCUhz58iPykfF668iUmJE045+eG4+9FfxMMwZ8jIusD0uNE5HAvbAwK5yP4AHv23ExMzAWMGvVM\nn9ghIuyp3kNSdBJp1rQ+aZW3ulq5c9mdFJ8uZulXlw7piYH9TU1zDcX1xe3FPCA0OhrJissiZ0RO\npyE7LrvTsVmXx0Wzqxmbw0aTs8kfbM4z6cBzbfle8Z4R8dhMfzw9Np1oU3C2aw01qpqqWHl0Je8d\nfo8Pjn5AXnwe14y7hitGGw6JOgp6YDqw/NKt6Z3HY9OJswyenelCBYfbwc82/YznPnuOrxV8jScu\nfYLE6L6ZA6U5P/rSta4SEVFK5QJtFyngbhF5pPem9i3nK/gOxwm2bJnClClrsFoLzuvZLtdpWloO\n+MJ+XK5a4uO/RGLiNZhMfbPERUR4+uOneW3Hayz/2nImp07uk/sON0SEbSe3sezgMpYdWkbx6WLG\njhzbpaCnxKQM6S7bUMftdbOhfAPvHX6P1cWrMYebDeG2nhHvQFGPs8QN+NDXUKemuYYn1z7J2/ve\n5pFLHuHbM78d1CEYTdf0peBvFpGZSqlioCTgVK6I9G69RhA4X8EHqKj4BVVVbzB16jpUFz/uIl4c\njjK/sDc37/fHvd5moqMn+MIFRESM4NSpD6ivX4PVOo2kpEUkJi4iOnpsb74iAH/a8yfuff9eXlv0\nGtflX9fr+/WEwdpFZ3fbWVO8hmUHl7H80HKiTFFcn389i/IXMTd7bkhNRhqsZTzY0OXce/ZW7+U7\nH3yHY6eP8dKVL7Fw/MJ2la3zLWOP10NpQymH6g5x7PQxrGarf6glIzaDWEsvNgQZYvRU8Lv8pROR\ntl1m/lNElgU84Npe2BeSZGTcTVXVHzlx4lekpX2D1tbD7VrsxvEgERHxflGPiSkgOdkYDjCbz96o\nIzPz3/F4Wjh9ejV1dcsoLX0Bk2kkiYmLSEq6nri4WSjV8/HBrxZ8lVHxo7jpzzdxqO4QD855ULdo\nOqG2pZZ3D73LskPLWHVsFZNSJrEofxGrvr6K/MR8XWYaTS+5MOVCVty2ghVHVvDgygf58cYf8/JV\nL3er91FEqGmp4VDdIQ7WHuRQ3SEOnTrkF/mUmBTGJ45ndPxomlxN7SZWRoRFtKsAtM25CIynWdNC\nqiIfKvTY016o0psWPkBz8162bp2NiJuoqFFER1/QrtUeHZ1PRMT5j/uJeLHZNlNbu4y6uuU4nVUk\nJi4kKWkRCQmXEx7eszW6pQ2lXPfmdczMmMn/XPs/uksNOFh70N9Vv6tqF5ePvpxF4xdxzbhrSI5J\nHmjzNJohi9vr5tdbf81THz/F9fnX88xlz5BqTcXmsHH41GFD0DuEiLAIxieO94f8xHzGJ45nzMgx\nXc5XEREaHA3+CkDbqpW21RVt6bbVKm0VgJy4HOblzOOyUZeREjMwOxwGg6C71g1Veiv4AC5XPeHh\nMX2ym965aG0tpq5uObW1y7DZNhEffymJiYtITFyIxZLerXvYHDZu/dut2Jw2/nrLX/vMJeZgwe11\ns75svV/km5xNLBq/iEX5i7hs1GVERvTfrlUajQbq7fU88/Ez/H7n74mMiKTeXs/YkWPbCfr4xPGM\nGzkuqBP+3F43lU2V/grAsdPH+Pj4x3xy/BNyRuSwYNQCFoxewPzc+YN6AqcW/EGIy1XPqVPvU1e3\njFOnVhAVNZ7ExOtISFiAxZKByZTa5bJBj9fDf636L5YeXMo7X3uH/KT8oNnZ3+OebbX5k7aTnGw6\n2e5Y1ljGR8UfkT0i2y/y09KnDfquej223D/ocg4uJ2wnWPfxOm6+9uaQmvTq9rrZemIrq4tXs7p4\nNZsqNlGQUsCCUQv40qgvMTd77qBqKPTZGL6m/zCZ4klN/RqpqV/D63XR0PAptbXLOHLkPpzOSpzO\nasLCIjGb0zCbUzGbUzGZUn3xNL477RJyrWbm/+5i3rjxD1w59pqB/kpfiFe81LbUdirkJ5vax01h\nJtJj00m3ppNmTSPdmk56bDpT06fy4pUvatfDGk0IkhGbQYo19Fa4RIRFMDtrNrOzZvPIJY9gd9v5\nvOxzVh9bzSOrH2FvzV5mZ872VwCmZ0wfUnMBdAt/ECAiuN31PvGvwuWqwulsC2fyNlQe5/GdNdw5\nOpL/NyrbXzEwmRKAcJSKCAjh3YhHtPtcbOx0YmIu6NRGr3g51XqKqqYqqpqrqGyq9Mermqva5dc0\n1xBnifMLuf8YGI81BN5qDt5GLxpNICJe3/9ZNS5X9TmPERHxzJp1iLAhJAjDnQZ7A58c/8TfA1De\nWM783Pn+CsCFyReGVC9iyHTpK6XGAM8A24AsoE5EnlFKPQlcGnDpsyKyyveZhzB25UsAPhCR5b78\nQuDbQDGQAiwWEU+H5w1Zwe8Jh+sOs/D/ruXyvIt4+uI78LhrcbvrEfEg4g44uoEz8Y7n2uIOt4PK\nlkZONDdQXLeFFpWF0zyFBrfZL+SVTZXUttRiNVtJtaaSGpNKqjWVtJi0dunAoyVi+GzFqhl4PJ5m\nWluP0NJyGLv9qK+y3F7AXa5awsNjMJlSMJtTznnctetq8vKeJjHxywP99TRBoqqpijUla1h9bDUf\nlXxEs7OZK8dc6Q8DPQEwlAR/BpAeINp7gX8BrhORpzq5fjawRESuVcZ6tf3AdKAJ2AUsEJFqpdSL\nwD4Rea3D57Xg+zjdeppb/nIL5nAzb37lzS4npbT5gT/Lw1yA29jalloyYjPIGZFD+HHFmEkRmB07\nSYqKIz/rnxifcQPpsZmkxKTolQJ9gB5bPn88nhZaW4/S2nrYt7T2sD/udtcTGTma6OhxREaOYdu2\nFubPn4vZnBwg5MmEhXX/HS4v/xmNjZ8zceL/BfFbDV6G4rt87PQxPjj6ASuPrmRN8RpGJ4zmqjFX\ncdXYq5ibPbfffwNDZgxfRLZ0yAoDmgGUUo8ADiAc+KmItAILgc99n/UopfYDRcA+IEpEqn33+Qy4\nDeibbe6GIAlRCbz3z+9x3/v3cfFrF/ODBT+gprmmSz/wfs9yccZxZuZMf166Nd3vT7ztH1jEQ23t\nMsrKfoiz7G1U9oOEx9wBaMHXnI3X60bE5XNqFRZw7HnXqMdjx24/2k7MW1uP0Np6GJerlsjIUURF\njSMqahyxsTNITf0aUVHjsFiy2jnVKi9fS1paUa++V0rKVykufhS3u7FXS3Y1g4fRCaO5Z8Y93DPj\nHlweFxsrNrLyyEoe/vBhDtYdZH7ufK4acxVXjrmScSPH9Wn3f6OjkYO1BzlQe4CDdcaxp/TL4JNS\n6kZghYgcVEq9DRSLSKtS6lvAT4G7gGSMVn0bjRjd9zWALSDf5ss/izvuuIO8vDwA4uPjKSws9Ncw\n165dCzBs0p99+hm3xNxCwfQCXl7/MqYyEynRKcy/dD63jLiFyj2VpOSncPUVV7f//MVn7neEI2QV\nZbU7D6BUOHv3JgD/zdSpJkpLf8jf/vYoSUnX85Wv/BCzOXnAv39/p9esWYNSKmTs6e/06tUrcDpP\nMnPmSFpbj7B27Sc4HBUUFJzC4ahgxw5BRJg61Rgr37HDC0BhoVEB2L4dlApj6lSTL+1FKcXUqRaU\nCmPbNjcgTJ7cSmRkLnv2jCQyMpOioi+RnPz/2Ly5DrM5mVmzFnTL3ra83n7/xMTLqKn5KwcPjhrQ\n8g/VdBuhYk8w0vNy5rEgbAEN2Q3Ys+ysPLqSJ3//JBFhEdzw5Ru4asxVmMpMWM3Wc95v/qXzKW0o\n5c/v/pnShlI8OR4O1h1k54adNLuayY7LxlJuIaIxghGWEfSUoE/aU0pdBlwvIvd3cm4C8J6IjFZK\nPQ04ReT7vnP/AH6D0cL/QETG+vJvAm4Vka90uJfu0h9AmpsPUF7+EjU1fyEl5WtkZT3YJ66E+xKP\np8U3yTEwVOP1tuD1OvB6HYg4fHF7J3ldX6NUBFbrFGJjZxIXN5PY2JlER0/o0lXzYMTlqsduP+rr\nNj/iC0bc5aojKmoUkZFjiIoaS1TUmWNkZF6nXeXG/6sXES/GlBwj3vVRfN3uoTNJrqbmb1RU/JTC\nwjUDbYomhBAR9tbs9Xf/f172OVNSp/i7/yckTeDIqSNGa732IAfqDnCg9gCH6w4zMmokE5ImMCFp\nAvmJ+cYxKZ+suKyzVj2EzBi+z5hrgXki8j2lVAaQC9woIg/7zl8H3CsiV3YYwzcBe4EZGC36XcDl\nIlKllHoJ2CMiv+vwLC34QSawRdQVDkclFRU/5eTJXxMfX0R29kPExc0Kmk1er9s38aqjkJ8dvF4n\nFku6b3mjEUymFMLDo1HKQljYmdB5OrLLa7xeJ01N27HZNtPYuAmbbTMuVy2xsdOIjZ3pD5GRuV/Y\nzdedMu5Z+bjwelvxelvxeFr98e6mnc6TflH3eu1niblxHIvFknlerqIHir4qZ6/XweefZzJjxlYi\nI3N7b9gQoq/f5cFMq6uVT45/4q8AHD191O+MKFDcxyeO79FeASEj+Eqp6cBaYDPGLnsxwM+BfCAa\nqAYmAY+LyBHfZxZjzNBPwGj5v+PLnwLcCxz3nVssRpU/8Hla8INMT/6B3e4mKitfpazsFSIjc8nO\nfojExGu61eIV8eJy1fmXHDqdlb6liJXt8pzOKtzuU0REJLYTcbM57SxhN5vTCA/v353UXK46bLYt\nNDZuxmYzgojLL/5xcbOIjZ2J2XxmhOqLylhE8Hgaz1qS2b58qvzl4vG0AkJYWBTh4VGEhUX54tH+\neMdzHdNmc4pf1E2mlJBaktQb+lKMDh36NhZLJrm5j/bJ/YYKWvC7RkT65H8pZAS/v9GCH5p4vW5q\nat6mrOyHeL12srO/Q2Tk6C8UcmN5VGyAWKe2O55xOpSOyZQUUl2858LhqAioAGzCZttCeHicfygg\nMnIULldNl6KuVEQ7p0tdlY3JNJKwsCiUMg0ZkQ5VGho2cODA7cyadUCXtaZf0YKvCUlEhPr6jygv\n/zFud0MHseooWCk9Wh41mBERWluP+HsA7PZS3xKxzkW9p5ssaYKPiLBpUz4XXPAGcXGzB9oczTBC\nC74maOguuuCjy7h/6OtyLin5Pk7nScaP/3mf3XOwo9/l4NNTwR86U4g1Go1mgEhNvY3q6rfweh0D\nbYpG0yW6ha/RaDR9wPbtRWRl/SfJyTcOtCmaYYJu4Ws0Gs0AkJb2daqq/jDQZmg0XaIFX9NtOnrP\n0vQ9uoz7h2CUc3LyzZw+vQans7bP7z0Y0e9y6KEFX6PRaPqAiIg4EhOvoabmrYE2RaPpFD2Gr9Fo\nNH1EXd0KSkqeYPr0jQNtimYYoMfwNRqNZoBISLgch6OU5uae72Sm0QQbLfiabqPH5IKPLuP+IVjl\nHBYWQUrKP1NV9UZQ7j+Y0O9y6KEFX6PRaPoQY7b+G3TY7kOjGXD0GL5Go9H0MZs3T2Hs2B+RkHDZ\nQJuiGcLoMXyNRqMZYPSafE0oogVf0230mFzw0WXcPwS7nFNS/pmamr/j8bQE9TmhjH6XQw8t+BqN\nRtPHWCzpjBgxh9rapQNtikbjR4/hazQaTRCoqnqTysrXmTJlxUCbohmihMz2uEqpMcAzwDYgC6gT\nkWeUUiOBHwDHgHHAIyJS7fvMQ0AskAB8ICLLffmFwLeBYiAFWCwing7P04Kv0WhCBo+nhfXrM5k5\ncy8WS8ZAm6MZgoTSpL0E4E0ReVFE7ge+qpSaBvw38KGIPA8sBV4EUErNBopEZAlwP/CSUipWKaWA\nN4DHROQHgAe4PYh2a7pAj8kFH13G/UN/lHN4eDRJSTdRVfV/QX9WKKLf5dAjaIIvIlvaWugBz2oG\nrgHW+/I+B671xRf60vha7/uBImA0ENXWCwB8FvAZjUajCVmM2fqvo3sfNaFAv0zaU0rdCKwQkYMY\nXfI236lGIEEpFQ4kA00BH2v0XZsccD2+eErQjdacRVFR0UCbMOTRZdw/9Fc5jxhxCW63jaamnf3y\nvFBCv8uhR0SwH6CUugy41NetD1CNMU7fCMQBp0XEo5Rqy28jDqgKuD4wv5pOuOOOO8jLywMgPj6e\nwsJC/0vX1r2k0zqt0zrdn+m0tH9h2bJnycz895CwR6cHb7otXlJSwvkQ1Fn6SqlrgXki8j2lVAaQ\nC3wd+EhE3lZKXQfcLCK3+8bwl4jItUopE7AXmIHRot8FXC4iVUqpl4A9IvK7Ds/Sk/aCzNq1a/0v\noCY46DLuH/qznFtaDrF9+3zmzCknLCzobayQQb/Lwaenk/aC9vYppaYDfwI2K6XWADHAz4BHgOeV\nUuOBMcBiABHZqJRao5R6FmPC34Mi0ui7123As0qp44ACXg+W3RqNRtOXREePJypqFKdPf0Bi4jUD\nbY5mGKPX4Ws0Gk2Qqaj4BfX1H3PhhX8aaFM0Q4hQWpan0Wg0GiAl5Z84dep9XK76gTZFM4zRgq/p\nNoETRzTBQZdx/9Df5WwyjSQh4XJqav7Sr88dSPS7HHpowddoNJp+IDX1X/QOepoBRY/hazQaTT/g\n9TpZvz6TadM2EhU1eqDN0QwB9Bi+RqPRhCBhYWaSk/+Jqqo/DrQpmmGKFnxNt9FjcsFHl3H/MFDl\nnJb2dSor/zAsXO3qdzn00IKv0Wg0/URs7EyUiqCxcf25L9Zo+hg9hq/RaDT9yPHj/43dXkp+/i8H\n2hTNIEeP4Ws0Gk0Ik5p6GzU1b+Px2AfaFM0wQwu+ptvoMbngo8u4fxjIco6MzMFqncKpU+8OmA39\ngX6XQw8t+BqNRtPPpKYak/c0mv5Ej+FrNBpNP+N221i/PpvZsw9jNicPtDmaQYoew9doNJoQJyIi\nlsTEhVRX6810NP2HFnxNt9FjcsFHl3H/EArlnJb29SHtajcUyljTHi34Go1GMwAkJCzA4ThBc/O+\ngTZFM0zQY/gajUYzQBw9+jBOZzWZmf9BZGQ2JlMKSnV7SFYzzOnpGL4WfI1Goxkg7PbjHDnyAHZ7\nCQ5HGW63DYsli8jIHCyWbP/RYskhMjIbiyWbiIi4gTZbEyKEjOArpdKA7wOTRWSWL+9J4NKAy54V\nkVW+cw8BsUAC8IGILPflFwLfBoqBFGCxiHg6eZ4W/CCzdu1aioqKBtqMIY0u4/4hVMvZ42nB4SjH\nbi/F4SjD4SjFbjeODkcZdnspSpkCKgKBlYIMTKZkX0giLMw0oN8lVMt4KNFTwY8Ioi0XA0uBKQF5\nIiKXdbxQKTUbKBKRa5VS4cB+pdRaoAl4A1ggItVKqReB24HXgmi3RqPRDAjh4dFER48nOnp8p+dF\nBLf79FkVgubm93E4TuBy1eJy1eB2nyI83IrJlNSuEmAyJWM2t0+35YWFRevhhCFOULv0lVJFwA9F\nZKYv/QTgAhxAOPBTEWlVSj0D2EXkWd91/wB+C+wDVorIWF/+jcBtIvKVTp6lW/gajUYDiHhxu+tx\nuWpwOmtwuWr8lYEzeWfSLlcNACZTMlFRY7Bap2K1TiM2dipRUfmEhQWzbag5X0Kphd8ZbwPFPpH/\nFvBT4C4gGdgfcF0jRvd9DWALyLf58jUajUbTBUqFYTKNxGQaSXR0/jmvFxG83haczhpaWw9hs22j\nrm45x48/hcNxkpiYAmJjp2G1TiU2dhoxMQWEhVn64Zto+pJ+FXwRCVx/sgZ4yBevxhi/byMOqOoi\nv7qr+99xxx3k5eUBEB8fT2FhoX8MqW1NqE6ff3rHjh3cf//9IWPPUEy35YWKPUM1/aMf/Uj/PgSk\nP/74Y386KiqPXbvMwEUUFRXhdjeyYsXvOHbsMAUF66io+Cmff34QiyWLoqL5WK1T2bFDERU1hgUL\nrvHfX/9eBOf3Ye3atZSUlHA+9HeX/gsi8rAvfh1wr4hc6RvDX+IbwzcBe4EZGC36XcDlIlKllHoJ\n2CMiv+vkWbpLP8is1ZNwgo4u4/5Bl3Pv8HjsNDfvpqlpOzbbNpqattPcvAeLJcvfC7BjRzhXX/0N\nTKaRA23ukCWUZunPB74OXAX8AngZWAJEY7TSJwGPi8gR3/WLMWboJwDvicg7vvwpwL3Acd+5xSLi\n7eR5WvA1Go1mgPB63bS0HKCpaTtNTdv8FQGTKRGrdTqxsdOIjZ2O1TodszlpoM0dEoSM4Pc3WvA1\nGo0mtBDx0tp6BJttKzbbVpqatmKzbSciIs4v/m0VAbM5daDNHXRowdcEDd0NGnx0GfcPupyDT1dl\nbFQCjvnEf5uvIrCNsLBoYmOn+yYHTic2djoWS3r/Gz6ICPVZ+hqNRqMZxigVRnT0WKKjx5KS8k+A\nsUrAbi/x9wJUVPwUm20rYWEmrNa21QFTsVqnEhk5SvsLOE90C1+j0Wg0IYeI4HCUYrNt980LMILb\nbcNqLfRXAKzWaURHTxiWvgJ0l75Go9FohixOZw1NTTt8EwONSoDDUU5MzIW+CoDRGxATM5nw8Kge\n319E8Hia8XhseDyNuN02X9yGx9OE12v3BUdAvKvQ+TVhYWaioycSE1PgCxcSHZ1PWJi5R7ZqwdcE\nDT3uGXx0GfcPupyDT3+WsdvdRHPzzna9AS0tB4iMHIXVOpWYmAsR8XQh4rYO6WbCwiIJD48lIiKW\n8PDAYCU8PIqwsMhzBqUsXZ7zeltobt5Hc/MeWlr20ty8B7u9hMjI0f4KQFtlICpqDIbH+bPRY/ga\njUajGVZERFgZMeJiRoy42J/n9Tppbt7rE//9KGXBZBpJZGSuX8A7CrqRtnYpsH1JTMyE8L77AAAH\nlUlEQVRE4GZ/2uOx09p6kOZmowJQWfl7mpv34HRWEh2dT0xMAdHRZyoCkZE5PX6mbuFrNBqNRhOi\nuN1NtLTsp7l5jy8YFQKPp4H585t0l75Go9FoNEMZl+s0ZvPIHgl+WDAN0gwtAv05a4KDLuP+QZdz\n8NFlHFxMpoQef0YLvkaj0Wg0wwDdpa/RaDQazSCkp7P0dQtfo9FoNJphgBZ8TbfRY3LBR5dx/6DL\nOfjoMg49tOBrNBqNRjMM0GP4Go1Go9EMQvQYvkaj0Wg0mrPQgq/pNnpMLvjoMu4fdDkHH13GoUfQ\nBF8plaaU+q1SalNA3kil1K+UUt/1nUsJOPeQUupppdRPlVLXBeQXKqV+rZT6nlLqFdUfTo41nbJj\nx46BNmHIo8u4f9DlHHx0GYcewdw852JgKTAlIO+/gQ9F5C9KqYXAi8DXlVKzgSIRudYn6PuVUmuB\nJuANYIGIVCulXgRuB14Lot2aLqivrx9oE4Y8uoz7B13OwUeXcegRtBa+iPwVQ7ADuQZY74t/Dlzr\niy/0pRERD7AfKAJGA1EiUu277rOAz2g0Go1Go+km/T2GnwLYfPFGIMHXok+mfeWg0XdtcsD1+OIp\naAaEkpKSgTZhyKPLuH/Q5Rx8dBmHHkFdlqeUKgJ+KCIzfelSYI6IVCilRgKHRSRRKfU04BSR7/uu\n+wfwG2Af8IGIjPXl3wTcKiJf6eRZek2eRqPRaIYVPVmWF8wx/M54F5gLvI0xxv9OQP4SAKWUCbgA\n+ASjRd+qlEoVkaoOn2lHT760RqPRaDTDjaC18JVS84GvA1cBvwBeBqKA54HjwBjguyJS47t+MZDg\nC++JyDu+/CnAvb7PJACLRcQbFKM1Go1GoxmiDBlPexqNRqPRaLqmv7v0+xyl1OXAjUA1ICLy9ACb\nNCRRSm0AWn1Jt4hcMZD2DAWUUmnA94HJIjLLlzcS+AFwDBgHPBKwSkXTQ7oo4yeBSwMue1ZEVg2A\neUMCpdQY4BlgG5AF1InIM/pd7ju+oIyfpAfv8qAWfKVUNMZwwUQRcSml/qKU+pKIfDTQtg1B3heR\npwbaiCFGt31VDIRxQ4TOylhE5LIBsmcokgC8KSLLAZRSe5VS7wL/hn6X+4quyrhH7/KgFnxgDnBc\nRFy+dNs6fS34fc8kpdTDGPMwNovIewNt0GBHRP7qW8kSyDUYNXkwfFO83q9GDTG6KGOUUo8ADiAc\n+KmItHa8RtM9RGRLh6wwoBn9LvcZX1DGPXqXB7vgB67rhzPr9zV9z/MislkpFQZ8opSyicinA23U\nEKQzXxVheqJqn/I2UCwirUqpbwE/Be4aYJuGBEqpG4EVInLQ5zpdv8t9TIcy7tG7PNg3z6kCYgPS\nI3x5mj5GRDb7jl7gU0B3iQaHas6803HAaf0D2beIyL6AVtAa4EsDac9QQSl1GXCpiDzgy9Lvch/T\nsYx7+i4PdsHfAOQqpcy+9FyMNf2aPkQpla+UujMgaxxwZKDsGeK0+aqAL/A7oTl/lFIvBCT1u9wH\nKKWuBa4UkfuVUhlKqTnod7lP6ayMe/ouD/pleb5Z+jcDNRje+p45x0c0PUQplQ78DNiOUVOPEJEH\nB9aqwU9PfVVoek4XZbwEiMZogU4CHhcRLfrniVJqOrAW2AwoIAbj92I5+l3uE7oo458D+fTgXR70\ngq/RaDQajebcDPYufY1Go9FoNN1AC75Go9FoNMMALfgajUaj0QwDtOBrNBqNRjMM0IKv0Wg0Gs0w\nQAu+RqPRaDTDAC34Gs0wQSl1f4f0ZqWUGohnazSa/kevw9dohglKqWIRGTXcnq3RaAwG++Y5Go2m\nGyilbgHilVJPAAeAFuAnQBGQAfwPsA5jx61C4IcY+yXMAO4Vka1KqTjgFeAwxp7cy0Tkgw7PuRi4\nzXfNLOAeIPDZG4BVwI8x9r0YAewQkT8qpe4DHvWds2J4EbtLRE4Ho0w0muGGbuFrNMOEjq1spdQa\n4HYRKfWJcZiIPKGU+k9guoh8XSl1A/AlEblPKfUDoFFEfqCUigL2A6MDN0RRSr0C1AHPAgXAURFp\nCXy2UupuYJqI3O0bUtgHXCIitUqpFiDJ95mHffGH+6N8NJqhjm7hazSaNo76jvWc2YSjnjM7nk0G\napVS3/WldwGJGPtYtPEsRit9E7Ae6EysJwHpAffZDaQBtUCNiLQE2HNpb76QRqM5gxZ8jWb44AFQ\nSk0WkV2+PBVw7CweyA6gUkR+6rvPrRit+UAuatu6Uyn1J+DLwFLA+//bu0OVCoIwDMPvVyyCzazF\nU0QsVu/AYDWLCN6CxaR4EG/BW7BYjTaDwW4yWkRBEH7DTBFMonhw3icOO7C75WP4d/n62jpwB7xV\n1Wlf2wYe+v7FJPNV9QJMgPtvP62kTwx8aRxXSc4AklwDS8B+kgtgE1hNcgNs0WbuK7R5/FqSDeAE\nmCY5BOaAxy/6zZeTnNPau15pDV8At0mOgWdag9o0yRHwDlBVl/26J2CvNzROgN0ffgfSsJzhS5oZ\nfs0v/R7/w5c0E5IcAAtJdv76XqT/yBO+JEkD8IQvSdIADHxJkgZg4EuSNAADX5KkARj4kiQNwMCX\nJGkAHzVReFYQVzO7AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb931fbac10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_index_paths(S)\n",
    "plt.savefig('../images/12_val/ES50_paths.pdf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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3jYC5RsDMzMwGpNaOgKRtJX1e0nxJp0l6b56/haSPSzpS0lmSZlWes0DSsZL+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\n6zB3BMzMzDrs/wN4cVxMVj7qHQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb931ebd750>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_index_histogram(S)\n",
    "plt.savefig('../images/12_val/ES50_histogram.pdf')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### European Options Valuation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%run 12_val/BCC97_valuation_comparison.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "      T |      K |      C0 |     MCS |    DIFF\n",
      "  0.083 |   3050 | 193.692 | 195.584 |   1.892\n",
      "  0.083 |   3225 |  62.147 |  64.162 |   2.016\n",
      "  0.083 |   3400 |   1.967 |   2.544 |   0.577\n",
      "  0.500 |   3050 | 259.126 | 272.960 |  13.834\n",
      "  0.500 |   3225 | 146.891 | 164.333 |  17.443\n",
      "  0.500 |   3400 |  67.142 |  85.330 |  18.188\n",
      "  1.000 |   3050 | 321.419 | 344.280 |  22.861\n",
      "  1.000 |   3225 | 216.227 | 243.415 |  27.188\n",
      "  1.000 |   3400 | 133.950 | 162.403 |  28.453\n",
      "  1.500 |   3050 | 378.978 | 407.035 |  28.057\n",
      "  1.500 |   3225 | 276.942 | 309.251 |  32.309\n",
      "  1.500 |   3400 | 193.333 | 227.887 |  34.554\n",
      "  2.000 |   3050 | 435.337 | 470.659 |  35.322\n",
      "  2.000 |   3225 | 335.010 | 374.315 |  39.305\n",
      "  2.000 |   3400 | 250.314 | 291.888 |  41.574\n",
      "  3.000 |   3050 | 549.127 | 594.413 |  45.287\n",
      "  3.000 |   3225 | 450.522 | 499.873 |  49.350\n",
      "  3.000 |   3400 | 364.049 | 416.300 |  52.252\n",
      "CPU times: user 6.25 s, sys: 203 ms, total: 6.45 s\n",
      "Wall time: 6.45 s\n"
     ]
    }
   ],
   "source": [
    "%time compare_values(M0=50, I=50000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "      T |      K |      C0 |     MCS |    DIFF\n",
      "  0.083 |   3050 | 193.692 | 195.870 |   2.178\n",
      "  0.083 |   3225 |  62.147 |  64.609 |   2.462\n",
      "  0.083 |   3400 |   1.967 |   2.606 |   0.639\n",
      "  0.500 |   3050 | 259.126 | 273.046 |  13.920\n",
      "  0.500 |   3225 | 146.891 | 164.698 |  17.807\n",
      "  0.500 |   3400 |  67.142 |  85.852 |  18.710\n",
      "  1.000 |   3050 | 321.419 | 342.696 |  21.277\n",
      "  1.000 |   3225 | 216.227 | 241.375 |  25.148\n",
      "  1.000 |   3400 | 133.950 | 160.706 |  26.756\n",
      "  1.500 |   3050 | 378.978 | 407.341 |  28.363\n",
      "  1.500 |   3225 | 276.942 | 309.124 |  32.182\n",
      "  1.500 |   3400 | 193.333 | 227.473 |  34.140\n",
      "  2.000 |   3050 | 435.337 | 470.323 |  34.986\n",
      "  2.000 |   3225 | 335.010 | 373.940 |  38.930\n",
      "  2.000 |   3400 | 250.314 | 291.583 |  41.268\n",
      "  3.000 |   3050 | 549.127 | 597.571 |  48.444\n",
      "  3.000 |   3225 | 450.522 | 503.362 |  52.840\n",
      "  3.000 |   3400 | 364.049 | 420.019 |  55.970\n",
      "CPU times: user 23.7 s, sys: 1.14 s, total: 24.9 s\n",
      "Wall time: 24.9 s\n"
     ]
    }
   ],
   "source": [
    "%time compare_values(M0=50, I=200000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "      T |      K |      C0 |     MCS |    DIFF\n",
      "  0.083 |   3050 | 193.692 | 193.241 |  -0.450\n",
      "  0.083 |   3225 |  62.147 |  61.595 |  -0.552\n",
      "  0.083 |   3400 |   1.967 |   2.581 |   0.614\n",
      "  0.500 |   3050 | 259.126 | 259.140 |   0.014\n",
      "  0.500 |   3225 | 146.891 | 149.090 |   2.199\n",
      "  0.500 |   3400 |  67.142 |  71.122 |   3.980\n",
      "  1.000 |   3050 | 321.419 | 322.117 |   0.697\n",
      "  1.000 |   3225 | 216.227 | 219.528 |   3.301\n",
      "  1.000 |   3400 | 133.950 | 139.285 |   5.335\n",
      "  1.500 |   3050 | 378.978 | 377.499 |  -1.479\n",
      "  1.500 |   3225 | 276.942 | 278.276 |   1.334\n",
      "  1.500 |   3400 | 193.333 | 197.137 |   3.804\n",
      "  2.000 |   3050 | 435.337 | 435.067 |  -0.270\n",
      "  2.000 |   3225 | 335.010 | 337.597 |   2.587\n",
      "  2.000 |   3400 | 250.314 | 255.541 |   5.227\n",
      "  3.000 |   3050 | 549.127 | 552.842 |   3.715\n",
      "  3.000 |   3225 | 450.522 | 457.774 |   7.252\n",
      "  3.000 |   3400 | 364.049 | 374.340 |  10.291\n",
      "CPU times: user 22.2 s, sys: 1.11 s, total: 23.3 s\n",
      "Wall time: 23.3 s\n"
     ]
    }
   ],
   "source": [
    "%time compare_values(M0=200, I=50000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### American Options Valuation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%run 12_val/BCC97_american_valuation.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%time lsm_compare_values(M0=150, I=50000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Chapter 13: Dynamic Hedging"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### BSM Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%run 13_dyh/BSM_lsm_hedging_algorithm.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "S, po, vt, errs, t = BSM_hedge_run(p=25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "plot_hedge_path(S, po, vt, errs, t)\n",
    "# plt.savefig('../images/13_dyh/BSM_hedge_run_1.pdf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "S, po, vt, errs, t = BSM_hedge_run(p=5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "plot_hedge_path(S, po, vt, errs, t)\n",
    "# plt.savefig('../images/13_dyh/BSM_hedge_run_2.pdf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%run 13_dyh/BSM_lsm_hedging_histogram.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%time pl_list = BSM_dynamic_hedge_mcs()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "plot_hedge_histogram(pl_list)\n",
    "plt.savefig('../images/13_dyh/BSM_hedge_histo.pdf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%time pl_list = BSM_dynamic_hedge_mcs(M=200, I=150000) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "plot_hedge_histogram(pl_list)\n",
    "# plt.savefig('../images/13_dyh/BSM_hedge_histo_more.pdf')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### BCC97 Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%run 13_dyh/BCC97_lsm_hedging_algorithm.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "S, po, vt, errs, t = BCC97_hedge_run(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "plot_hedge_path(S, po, vt, errs, t)\n",
    "plt.savefig('../images/13_dyh/BCC_hedge_run_1.pdf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "S, po, vt, errs, t = BCC97_hedge_run(8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "plot_hedge_path(S, po, vt, errs, t + 1)\n",
    "plt.savefig('../images/13_dyh/BCC_hedge_run_2.pdf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "S, po, vt, errs, t = BCC97_hedge_run(4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "plot_hedge_path(S, po, vt, errs, t + 1)\n",
    "plt.savefig('../images/13_dyh/BCC_hedge_run_3.pdf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%run 13_dyh/BCC97_lsm_hedging_histogram.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%time pl_list = BCC97_hedge_simulation(M=150, I=150000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "plot_hedge_histogram(pl_list)\n",
    "plt.savefig('../images/13_dyh/BCC_hedge_histo.pdf')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"http://hilpisch.com/tpq_logo.png\" alt=\"The Python Quants\" width=\"35%\" align=\"right\" border=\"0\"><br>\n",
    "\n",
    "<a href=\"http://www.pythonquants.com\" target=\"_blank\">www.pythonquants.com</a> | <a href=\"http://twitter.com/dyjh\" target=\"_blank\">@dyjh</a>\n",
    "\n",
    "<a href=\"mailto:analytics@pythonquants.com\">analytics@pythonquants.com</a>\n",
    "\n",
    "**Python Quant Platform** |\n",
    "<a href=\"http://quant-platform.com\">http://quant-platform.com</a>\n",
    "\n",
    "**Derivatives Analytics with Python** |\n",
    "<a href=\"http://www.derivatives-analytics-with-python.com\" target=\"_blank\">Derivatives Analytics @ Wiley Finance</a>\n",
    "\n",
    "**Python for Finance** |\n",
    "<a href=\"http://python-for-finance.com\" target=\"_blank\">Python for Finance @ O'Reilly</a>"
   ]
  }
 ],
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